Dempsey said Wednesday that the assistance would not involve sending U.S. combat troops, but could involve the U.S. sending in training teams and accelerating sales of weapons and equipment.

The last American combat troops left Iraq in December 2011, ending a nearly nine-year war that cost nearly 4,500 American and more than 100,000 Iraqi lives.

About 100 military and civilian Defense Department personnel remain in Iraq as an arm of the American Embassy to act as liaisons with the Iraqi government and facilitate arms sales. The U.S. has similar offices in other countries.

Ali al-Moussawi, the media adviser for Iraqi prime minister Nouri al-Maliki, told The Associated Press that Baghdad would welcome increased arms sales and faster weapons deliveries along with U.S. training teams to help it confront rising regional instability and terrorist threats.

Iraq is struggling to contain a resurgent al-Qaida that is one of the main drivers behind the country’s worst uptick in violence in half a decade. More than 2,000 people have been killed in car bombings and other violent attacks in Iraq since the start of April.

“We welcome this kind of cooperation and we consider it a part of the existing agreement between us,” al-Moussawi said when asked about Dempsey’s comments.

“Because of the high risks the region faces, I think there should be bigger cooperation and coordination between all countries threatened by terrorism.”

Iraqi fighters have traveled to fight on both sides of Syria’s civil war. The Iraqi branch of al-Qaida is pushing to make itself a player in the conflict and now calls itself the Islamic State of Iraq and the Levant to highlight its cross-border ambitions.

Iraq has acquired billions of dollars’ worth of American-made military equipment, including howitzers, armored personnel carriers and Abrams tanks in recent years.

It has yet to receive the first of as many as 36 F-16 fighter jets it has ordered, and Baghdad has been pressing U.S. officials to speed delivery of the warplanes.

Also on Thursday, a spokesman for Iraq’s Independent High Electoral Commission said a voting list backed by influential Sunni politicians has won the biggest single bloc of seats in provincial elections in the Sunni-dominated province of Anbar.

Safaa al-Moussawi, a spokesman for the commission, said the United list led by Iraqi Parliament Speaker Osama al-Nujaifi won eight of 30 seats in Anbar’s provincial council. A bloc backed by al-Maliki came in second with five seats.

The western province of Anbar, a former al-Qaida stronghold, has been the center of anti-government rallies protesting what Sunnis say is their second-class treatment by the Shiite-led government.

Residents in Anbar and neighboring Ninevah province voted last week in local elections that had been delayed due to security concerns.